Reliability evaluation of phased-mission systems with load-sharing components

Many real world systems operate in phased-missions where the reliability structure varies over consecutive time periods, known as phases. For mission success, all phases must be completed without failure. During each mission phase, the system or its subsystems may be subject to different loads (stresses) and environmental conditions. Therefore, the failure (hazard) rate of components can change with phases due to the phase-dependent variations in the loads. In addition, in the majority of applications, the subsystems within a system operate in a load-sharing configuration where the total load on a subsystem is shared by all of its working components. Therefore, upon a failure of a component within a subsystem, the load on the surviving components increases. This in turn induces higher component failure rates, which introduces complex dynamic dependencies among the load-sharing components. Further complicating the analysis are statistical dependencies across the phases for a given component. For example, the state of a component at the beginning of a new phase is identical to its state at the end of the previous phase. The consideration of these dynamic dependencies poses unique challenges to existing reliability evaluation algorithms. In this paper, we propose an efficient recursive algorithm for reliability evaluation of phased-mission systems with load-sharing components. In the analysis, we considered multiple subsystems where each subsystem can have multiple load-sharing components. The proposed algorithm is developed based on: (1) a modularization technique, (2) an easily computable closed-form expression for conditional reliability of load-sharing subsystems, and (3) a recursive formula for the reliabilities of subsystems across the phases. The reliability evaluation algorithm is illustrated using an example.